A little Maths I learned…

I spent a good chunk of my time teaching maths at primary level, and although, admittedly, mainly at Key Stage 2 level, I like to think I was reasonably successful at it. I love teaching Maths, and I think it can be beautiful in its simplicity, and the patterns that can be found and the comparisons that can be made can sometimes blow your mind. The links to music and nature can astound, and finding ratios and threads that run through many different aspects of life can be eye-opening.

I found it is the same with the children – it is possible to blow their mind with Maths and in an excellent way. So many children have a negative view of maths or fear it. The reasons for this can be plentiful. Typically, they have had a bad experience with the subject or have found themselves confused by it. It may be there have been given a negative view of maths by someone near to them. We’ve all had the parent who says ‘I wasn’t good at Maths, so they won’t be’. It frustrates and infuriates me – there is no reason for it to follow like that, and very much like the language we have seen around Covid and catch up, it can become a self-fulfilling prophecy. 

I loved blowing the children’s minds with maths stories I’d seen in the news. There were some great ones. The mathematicians who found a new prime number and the ones who found a new tessellating pentagon were two that always stuck in my mind. We looked these up as a class, we read the stories, and it opened up so much language and discussion; it was amazing! We all learned something! We often read a child a text or a piece of writing and tell them how brilliant it is, or find they get lost in it, enthralled and rapt in it, but we can do the same with Maths. It’s like they are being let into a bit of secret that no-one else knows, and they love it. 

But what makes for good teaching of maths? Here is what I’ve picked up over the years.

Don’t tell them they can’t do it.

I know this might cause a bit of disagreement, but forewarning them, it might be hard or that lots of people find it tricky can be the kiss of death before children have even started. I’ve seen teachers tell classes that fractions are coming and that lots of people struggle at first and not to worry if you don’t understand it. 

Now, I get the thinking behind that – they shouldn’t be demoralised if they don’t understand on the first pass through. But straight away, some will decide they can take it as the easy option or switch off. I also agree that sometimes you can over exaggerate. ‘Now this Maths will be tough, but I know you guess will ace it!’. A lot comes down to knowing your class and your children. I feel very strongly that there is enough negativity around maths for some children, and being told they’re going to struggle with it before they have even started is dangerous. Do we do this with other subjects? I think we sometimes see that Maths can confuse and try to protect the children from struggling, but is this the best way to do this? A better way to ensure they understand is to work harder at clear explanations and simple language to make it as accessible as possible, surely?

Must Get the Basics

I’ve also come across several children who have been building on quicksand when they have got towards the end of Key Stage 2. They haven’t got the basics of the subject down or got them as known facts. Some things make things easier. Take times tables, for example. If you can get secure knowledge of these by, let’s say, Y4, then the upper Key Stage 2 curriculum becomes more accessible. It bleeds into so many areas:

Written multiplication, short and long division, simplifying fractions, adding fractions, decimals, percentages, ratio, probability, proportion, converting units of length, and there are probably more. If you know your time tables, instantly these areas become easier to deal with as you are only having to deal with the new information and methods, not worrying about the times tables. 

Place value is another one – it has to be secure because it feeds into so much. The time spent on these aspects is worth it because you cannot build the following steps. If you need to condense some other topics, then so be it because these basics of number bonds, quick calculations, place value, timetables, and certain conversions make everything so much easier at the primary level by the time you reach the top of the school. EYFS and Key Stage 1 teachers have such an essential job building the blocks that everything else comes from. 

Understanding, not tricks

Following that is the idea that you can’t just give a trick to do something (the classic, adding a zero!). Maths shouldn’t be taught as a subject of tricks to loophole your way around actually doing what is needed. It is a surefire way to build misconceptions and devalue the real understanding needed for future concepts where such tricks may not exist. I was always at pains to explain to the children I taught where they could come unstuck using such shortcuts if they didn’t understand why they were doing it. When I was sure they had grasped it, I would explain why they did work and why they didn’t give the complete picture.

As Maths works in the abstract, sometimes you have to work with what you do know about something to work out what you don’t know, and if you haven’t got the steps to fall back on, then it can be hard to unpick what has gone wrong. This is key to children becoming independent and transferring their skills from one area of the subject to another. 

Use the correct language.

If you’re teaching them something, tell them the right things. It means they are exposed to it straight away, removing some of the fear that can go with it. If, in Year 2, they are doing 6+?=8, then tell them they are doing algebra. If they are working with 3D shapes, call them vertices right from the word go. We want our scientists to use the correct language, and we should expect the same from our mathematicians. We expect precise work in other areas; let’s expect it from the language we use too. Have high expectations of them. Use numerator and denominator as soon as fractions are introduced. Of course, explain what they mean clearly and use a simplified version to support their understanding and give them the actual terms. They will encounter them as they move through school, and that drip, drip of the language will stand them in good stead. 

Give proper support.

Manipulative and concrete resources are so important. Maths is abstract, and without being able to visualise the numbers, some will find it tricky. Use them at every opportunity. No child is too old to use them or should feel embarrassed to do so. We give word mats and vocal lists in English; these are the maths equivalents. Let them play, let them build, let them experiment and see what they can do. How many nets of a cube can they make using polydron? It will give a much better idea of how a net folds up if they have done it with concrete resources and better equip them to build on it. Looking at volume? Build the shape out of multilink to show precisely how the middle of that shape is filled up and why the volume is what it is. 

Resourcing is also about our teaching. Keep it simple. Use the correct language, as I’ve already said, but break it into simple steps where each part is explained thoroughly as to why it is being done and why it works. Give them step by step examples to look through, keep good quality models on the board wherever you can. If you’re modelling and are supposed to write the method in books with squared paper, model it on squared paper. Let them see exactly what they need to do. Talk it through, verbalise your thinking talk it through. Model and tell them how you add 15 and 17 in your head. If they haven’t got all the basics as known facts and are starting something new, then give them the support. If they are making equivalent fractions and tables are a struggle, give them a times tables and division square. Why make it harder for them than it needs to be? Let them focus on the new things and not have to worry about something that might stand in their way until they are secure in their understanding of the new method. 

Get those basic steps right before moving them on. Maths is so sequential that by skipping them forward, you are doing them no favours at all. 

Expose them to higher-level concepts when you can

I am really in favour of dripping in higher bits of knowledge where you can. I was covering a Year 2 class, and we were playing with numbers as a starter – they had to tell me all the facts they could think of about the number 4. One of them said to me that it was 2 x 2. ‘Brilliant!’ I replied. I then asked them if they knew what numbers were called when you multiplied the number by itself? They looked at but sheepish, but they had done work on arrays previous and learned a bit about tables. We talked about square numbers linked to the arrays they’d been working on and saw the patterns. Are square numbers on the Year 2 curriculum? No. Will they all remember it? No. Will a bit of it catch for some of them? Yes! This is the key for me, little drips of language and concepts like pieces of a jigsaw, and when they meet them again, they can build the whole picture that little bit easier. Not to mention, they love finding out things they feel are a bit out of their reach or something they shouldn’t know yet. The example I gave built on their prior knowledge and related to what they did know. I’m not advocating dripping in a bit of trigonometry. This is where teacher subject knowledge is so necessary too – not just knowing your curriculum but also what comes before and after.

Make time for games and fun.

https://secretheadteacher.org/2019/08/26/17-maths-warm-up-games/

There are so many great games, websites, apps and other resources to make maths enjoyable. They don’t need to be number related – problem-solving games are just as much use. They teacher logical and organised thinking, step by step problem solving and encourage good habits – a great example of this is the Traffic Jam game where you have to move the cars around to release the red car out the exit. Games like Countdown are just great for manipulating numbers and playing with them. Give them help – write out the 75 times table for them, for example, but just one number may have several different ways of reaching the solution, so much discussion can come out of it. They also self-correct – they get halfway through their explanation and say, ‘oh, that doesn’t work!’. I wrote another blog with some ideas of games and starters here:

I loved using these games, and they are all adaptable. 

So, teaching maths. It’s brilliant. It’s a whole world and one we need to teach them not to be scared of. We need to show them it isn’t dull, and it isn’t too complicated or incomprehensible. I loved seeing the progress they made and watching them turn from maths haters into maths lovers. That’s the power we have as a teacher, and it feels great when it happens. 

Published by @secretHT1

Primary HT. Using this as a space to write honestly and freely about the state of education currently.

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